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find the absolute max and min of the function z = f (x, y ) = x 2 +y 2 − 4x − 4y on the closed disk x 2 + y 2 ≤ 9

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find the absolute max and min of the function z = f (x, y ) = x 2 +y 2 − 4x − 4y on the closed disk x 2 + y 2 ≤ 9. (a) Find critical points of f in the open disk x 2 + y 2 < 9. (b) Explain why the problem of finding the absolute maximum and minimum of the function f (x, y ) = x 2 + y 2 − 4x − 4y on the circle x 2 + y 2 = 9 is the same as the problem of finding the absolute maximum and minimum of the function h(x, y ) = 9 − 4x − 4y on the circle x 2 + y 2 = 9. (c) To solve the problem of optimizing the function z = h(x, y ) on the circle x 2 + y 2 = 9 you can just use the geometric approach outlined above. The symmetry of the problem will enable you to find the exact locations of the critical points!